Temporal Difference Flows

Predictive models of the future are fundamental for an agent's ability to reason and plan. A common strategy learns a world model and unrolls it step-by-step at inference, where small errors can rapidly compound. Geometric Horizon Models (GHMs) offer a compelling alternative by directly making predictions of future states, avoiding cumulative inference errors. While GHMs can be conveniently learned by a generative analog to temporal difference (TD) learning, existing methods are negatively affected by bootstrapping predictions at train time and struggle to generate high-quality predictions at long horizons. This paper introduces Temporal Difference Flows (TD-Flow), which leverages the structure of a novel Bellman equation on probability paths alongside flow-matching techniques to learn accurate GHMs at over 5x the horizon length of prior methods. Theoretically, we establish a new convergence result and primarily attribute TD-Flow's efficacy to reduced gradient variance during training. We further show that similar arguments can be extended to diffusion-based methods. Empirically, we validate TD-Flow across a diverse set of domains on both generative metrics and downstream tasks including policy evaluation. Moreover, integrating TD-Flow with recent behavior foundation models for planning over pre-trained policies demonstrates substantial performance gains, underscoring its promise for long-horizon decision-making.

Simple Ingredients for Offline Reinforcement Learning

Offline reinforcement learning algorithms have proven effective on datasets highly connected to the target downstream task. Yet, leveraging a novel testbed (MOOD) in which trajectories come from heterogeneous sources, we show that existing methods struggle with diverse data: their performance considerably deteriorates as data collected for related but different tasks is simply added to the offline buffer. In light of this finding, we conduct a large empirical study where we formulate and test several hypotheses to explain this failure. Surprisingly, we find that scale, more than algorithmic considerations, is the key factor influencing performance. We show that simple methods like AWAC and IQL with increased network size overcome the paradoxical failure modes from the inclusion of additional data in MOOD, and notably outperform prior state-of-the-art algorithms on the canonical D4RL benchmark.

Layered State Discovery for Incremental Autonomous Exploration

We study the autonomous exploration (AX) problem proposed by Lim & Auer (2012). In this setting, the objective is to discover a set of $\epsilon$-optimal policies reaching a set $\mathcal{S}_L^{\rightarrow}$ of incrementally $L$-controllable states. We introduce a novel layered decomposition of the set of incrementally $L$-controllable states that is based on the iterative application of a state-expansion operator. We leverage these results to design Layered Autonomous Exploration (LAE), a novel algorithm for AX that attains a sample complexity of $\tilde{\mathcal{O}}(LS^{\rightarrow}_{L(1+\epsilon)}\Gamma_{L(1+\epsilon)} A \ln^{12}(S^{\rightarrow}_{L(1+\epsilon)})/\epsilon^2)$, where $S^{\rightarrow}_{L(1+\epsilon)}$ is the number of states that are incrementally $L(1+\epsilon)$-controllable, $A$ is the number of actions, and $\Gamma_{L(1+\epsilon)}$ is the branching factor of the transitions over such states. LAE improves over the algorithm of Tarbouriech et al. (2020a) by a factor of $L^2$ and it is the first algorithm for AX that works in a countably-infinite state space. Moreover, we show that, under a certain identifiability assumption, LAE achieves minimax-optimal sample complexity of $\tilde{\mathcal{O}}(LS^{\rightarrow}_{L}A\ln^{12}(S^{\rightarrow}_{L})/\epsilon^2)$, outperforming existing algorithms and matching for the first time the lower bound proved by Cai et al. (2022) up to logarithmic factors.

On the Complexity of Representation Learning in Contextual Linear Bandits

In contextual linear bandits, the reward function is assumed to be a linear combination of an unknown reward vector and a given embedding of context-arm pairs. In practice, the embedding is often learned at the same time as the reward vector, thus leading to an online representation learning problem. Existing approaches to representation learning in contextual bandits are either very generic (e.g., model-selection techniques or algorithms for learning with arbitrary function classes) or specialized to particular structures (e.g., nested features or representations with certain spectral properties). As a result, the understanding of the cost of representation learning in contextual linear bandit is still limited. In this paper, we take a systematic approach to the problem and provide a comprehensive study through an instance-dependent perspective. We show that representation learning is fundamentally more complex than linear bandits (i.e., learning with a given representation). In particular, learning with a given set of representations is never simpler than learning with the worst realizable representation in the set, while we show cases where it can be arbitrarily harder. We complement this result with an extensive discussion of how it relates to existing literature and we illustrate positive instances where representation learning is as complex as learning with a fixed representation and where sub-logarithmic regret is achievable.

Improved Adaptive Algorithm for Scalable Active Learning with Weak Labeler

Active learning with strong and weak labelers considers a practical setting where we have access to both costly but accurate strong labelers and inaccurate but cheap predictions provided by weak labelers. We study this problem in the streaming setting, where decisions must be taken \textit{online}. We design a novel algorithmic template, Weak Labeler Active Cover (WL-AC), that is able to robustly leverage the lower quality weak labelers to reduce the query complexity while retaining the desired level of accuracy. Prior active learning algorithms with access to weak labelers learn a difference classifier which predicts where the weak labels differ from strong labelers; this requires the strong assumption of realizability of the difference classifier (Zhang and Chaudhuri,2015). WL-AC bypasses this \textit{realizability} assumption and thus is applicable to many real-world scenarios such as random corrupted weak labels and high dimensional family of difference classifiers (\textit{e.g.,} deep neural nets). Moreover, WL-AC cleverly trades off evaluating the quality with full exploitation of weak labelers, which allows to convert any active learning strategy to one that can leverage weak labelers. We provide an instantiation of this template that achieves the optimal query complexity for any given weak labeler, without knowing its accuracy a-priori. Empirically, we propose an instantiation of the WL-AC template that can be efficiently implemented for large-scale models (\textit{e.g}., deep neural nets) and show its effectiveness on the corrupted-MNIST dataset by significantly reducing the number of labels while keeping the same accuracy as in passive learning.

Scalable Representation Learning in Linear Contextual Bandits with Constant Regret Guarantees

We study the problem of representation learning in stochastic contextual linear bandits. While the primary concern in this domain is usually to find realizable representations (i.e., those that allow predicting the reward function at any context-action pair exactly), it has been recently shown that representations with certain spectral properties (called HLS) may be more effective for the exploration-exploitation task, enabling LinUCB to achieve constant (i.e., horizon-independent) regret. In this paper, we propose BanditSRL, a representation learning algorithm that combines a novel constrained optimization problem to learn a realizable representation with good spectral properties with a generalized likelihood ratio test to exploit the recovered representation and avoid excessive exploration. We prove that BanditSRL can be paired with any no-regret algorithm and achieve constant regret whenever an HLS representation is available. Furthermore, BanditSRL can be easily combined with deep neural networks and we show how regularizing towards HLS representations is beneficial in standard benchmarks.

Contextual bandits with concave rewards, and an application to fair ranking

We consider Contextual Bandits with Concave Rewards (CBCR), a multi-objective bandit problem where the desired trade-off between the rewards is defined by a known concave objective function, and the reward vector depends on an observed stochastic context. We present the first algorithm with provably vanishing regret for CBCR without restrictions on the policy space, whereas prior works were restricted to finite policy spaces or tabular representations. Our solution is based on a geometric interpretation of CBCR algorithms as optimization algorithms over the convex set of expected rewards spanned by all stochastic policies. Building on Frank-Wolfe analyses in constrained convex optimization, we derive a novel reduction from the CBCR regret to the regret of a scalar-reward bandit problem. We illustrate how to apply the reduction off-the-shelf to obtain algorithms for CBCR with both linear and general reward functions, in the case of non-combinatorial actions. Motivated by fairness in recommendation, we describe a special case of CBCR with rankings and fairness-aware objectives, leading to the first algorithm with regret guarantees for contextual combinatorial bandits with fairness of exposure.

Reaching Goals is Hard: Settling the Sample Complexity of the Stochastic Shortest Path

We study the sample complexity of learning an $\epsilon$-optimal policy in the Stochastic Shortest Path (SSP) problem. We first derive sample complexity bounds when the learner has access to a generative model. We show that there exists a worst-case SSP instance with $S$ states, $A$ actions, minimum cost $c_{\min}$, and maximum expected cost of the optimal policy over all states $B_{\star}$, where any algorithm requires at least $\Omega(SAB_{\star}^3/(c_{\min}\epsilon^2))$ samples to return an $\epsilon$-optimal policy with high probability. Surprisingly, this implies that whenever $c_{\min}=0$ an SSP problem may not be learnable, thus revealing that learning in SSPs is strictly harder than in the finite-horizon and discounted settings. We complement this result with lower bounds when prior knowledge of the hitting time of the optimal policy is available and when we restrict optimality by competing against policies with bounded hitting time. Finally, we design an algorithm with matching upper bounds in these cases. This settles the sample complexity of learning $\epsilon$-optimal polices in SSP with generative models. We also initiate the study of learning $\epsilon$-optimal policies without access to a generative model (i.e., the so-called best-policy identification problem), and show that sample-efficient learning is impossible in general. On the other hand, efficient learning can be made possible if we assume the agent can directly reach the goal state from any state by paying a fixed cost. We then establish the first upper and lower bounds under this assumption. Finally, using similar analytic tools, we prove that horizon-free regret is impossible in SSPs under general costs, resolving an open problem in (Tarbouriech et al., 2021c).

Top $K$ Ranking for Multi-Armed Bandit with Noisy Evaluations

We consider a multi-armed bandit setting where, at the beginning of each round, the learner receives noisy independent, and possibly biased, \emph{evaluations} of the true reward of each arm and it selects $K$ arms with the objective of accumulating as much reward as possible over $T$ rounds. Under the assumption that at each round the true reward of each arm is drawn from a fixed distribution, we derive different algorithmic approaches and theoretical guarantees depending on how the evaluations are generated. First, we show a $\widetilde{O}(T^{2/3})$ regret in the general case when the observation functions are a genearalized linear function of the true rewards. On the other hand, we show that an improved $\widetilde{O}(\sqrt{T})$ regret can be derived when the observation functions are noisy linear functions of the true rewards. Finally, we report an empirical validation that confirms our theoretical findings, provides a thorough comparison to alternative approaches, and further supports the interest of this setting in practice.

Privacy Amplification via Shuffling for Linear Contextual Bandits

Contextual bandit algorithms are widely used in domains where it is desirable to provide a personalized service by leveraging contextual information, that may contain sensitive information that needs to be protected. Inspired by this scenario, we study the contextual linear bandit problem with differential privacy (DP) constraints. While the literature has focused on either centralized (joint DP) or local (local DP) privacy, we consider the shuffle model of privacy and we show that is possible to achieve a privacy/utility trade-off between JDP and LDP. By leveraging shuffling from privacy and batching from bandits, we present an algorithm with regret bound $\widetilde{\mathcal{O}}(T^{2/3}/\varepsilon^{1/3})$, while guaranteeing both central (joint) and local privacy. Our result shows that it is possible to obtain a trade-off between JDP and LDP by leveraging the shuffle model while preserving local privacy.